Comparators are well known in the field of electronics. A typical comparator has two input terminals (a first input terminal and a second input terminal) and an output terminal. The voltages on the two input terminals are compared and the output depends on which of the two input voltages is greater. For example, if the input on the first terminal is larger than the input on the second terminal, the output is 2.5 volts (logic level 1); while if the input on the second terminal is greater than that on the first terminal, the output is -2.5 volts (logic level 0). The use of comparators is well known in the art of electronic signaling. For example, in the telecommunications industry, comparators are employed to recover signals that have been degraded by noise. FIGS. 1A, 1B and 1C are provided to illustrate how a data recovery process works. FIG. 1A shows a stream of digital data in the form of an ideal square wave with a peak to peak value of 5 volts. The square wave is used to represent data generated by a differential signaling digital source, such as a computer. The data may be transmitted to a digital receiver through any number of possible transmission media, such as copper wire, fiber optic lines, coaxial cable, or wireless links. Regardless of the media used, the data signal will be attenuated by the media and corrupted by noise as it travels to the receiver.
FIG. 1B shows the signal of FIG. 1A as it appears upon arrival at a receiver. For purposes of illustration, the received signal is modeled as a sine wave of period 2T, although in practice the received signal is likely to have a more irregular shape. To recover the original data from the received signal, one input terminal of a comparator is coupled to the received signal while the other input terminal of the comparator is coupled to a reference (e.g. 0 volts). The comparator then compares samples of the received signal to the reference. If a sample is greater than the reference, the output of the comparator is 2.5 volts (logic level 1), and if a sample is less than the reference, the output of the comparator is -2.5 volts (logic level 0). This sampling technique works best if the received signal is sampled at its peaks and valleys, since sampling at the peaks and valleys provides the greatest differential between the samples and the reference, and thus the greatest margin for error. However, the time of arrival of the signal is generally not known, and therefore sampling at the peaks and valleys can not be assured.
FIG. 1C illustrates the sampling of a received signal. As can be seen from the figure, a first sample 10 occurs just before the received waveform has crossed the 0 voltage point. The remaining samples occur regularly at periodic intervals following the first sample. Since the frequency of the original signal may be known a priori, the sampling frequency may be set to match the original frequency. Thus, once the first sample is adjusted such that it occurs at a peak or valley, the remaining samples will also occur at peaks or valleys. A method that is commonly used to find the peak and valley points of a received signal is to find the zero crossing point of the signal and then take the first sample at a point that is one quarter period removed from the zero crossing point.
Detection of the zero point may be accomplished through successive approximation. Upon taking of the first sample in FIG. 1C, the output of the comparator should be logic level 1 (2.5 volts) since the sample value is greater than the reference value of 0 volts. Normally, the second sample (1 period later) would again occur just before the received signal dipped below zero (sample 12). However, if the sampling time of the second sample were shifted right (sample 14), the second sample would occur just after the received waveform dipped below zero, and therefore the output of the comparator for the second sample would be -2.5 volts, thereby indicating that the zero crossing occurred some time between the time at which the unshifted second sample would have occurred and the time at which the second sample was actually taken. If the amount of shift is made small a zero crossing might not occur before the second sample. Accordingly, a small shift may be applied to successive samples until a zero crossing is detected; the smaller the shift, the more accurate the determination of the time of zero crossing.
The above-described zero crossing detection scheme is limited by the comparator's ability to respond to a zero crossing. The comparator output does not change instantaneously when the relative levels of the comparator inputs require that the output change. For example, when a comparator is comparing a received signal to a 0 volt reference and the received signal changes from a positive value (output is 2.5 volts) to a negative value (output should be -2.5 volts), the output does not change instantly to 2.5 volts. The received signal must be negative for some period of time (the "response time") before the comparator output changes from 2.5 volts to -2.5 volts. Therefore, the precision in detecting the time of zero crossing can only be as great as the response time of the comparator. Currently comparator response times are on the order of 4 ns.